Assumptions

Boats

  1. Mixgears are all classified as dropliners
  2. The boats in Pagatan (2) are ignored
  3. Ignore Nano Boats (total guessed landings \(291.0\) tonnes)

This leaves a 5 populations problem:

class Dropline Longline
Big NA 24
Medium 38 68
Small 635 12

If we assume that within these 5 populations, all boats are the same, we can guess:

class fishing_gear GT landings
Big Longline 42.583333 1533.0
Medium Dropline 17.210526 981.0
Medium Longline 26.838235 2737.5
Small Dropline 8.445669 8044.5
Small Longline 11.083333 199.5

You can see that 3 populations really matter the most, Small dropliners, Medium longliners and Big Longiners. They make up 91.2% of the landings.

  1. We focus on 3 populations

Biological

  1. There is only one species of fish: Snapper
  2. Snapper lives between 100-400 meters deep

Parameters

Boats

Population 1: Small Dropliners

The biggest population by far, and accounting for about 60% of the landings in 712.
They are organized over 4 ports, with Sumenep and Brondong being the most important.

Registration Port Frequency
Gili Iyang 2
PP. Brondong 163
PP. Tanjung Pandan 16
Sumenep 454

Rest Time & Yearly Effort

Assume max 200 days out (4800 hours), no seasonality

Max Trip Length

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    6.00   10.00   12.00   11.95   13.75   20.00       2

Size of hold

Use formula from hold_size.pdf:

## [1] 1938.128

Which I will round to 1940.

We can also look at their income targets as a function of hold size:

##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max.      NA's 
##    0.2857    0.5179    0.5714    0.6389    0.7143    1.0714 0.0034286

This would mean that approximately 63% of a load is enough to hit the targets.

Variable Cost

From the survey, it looks variable costs are about 1 MIL$/day

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   0.500   1.000   1.000   1.107   1.238   2.500       2
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   20833   41667   41667   46117   51562  104167       2

In fact we can just run a regression and be done with it:

## 
## Call:
## lm(formula = `Operational Costs ($/day)` ~ GT, data = survey)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7324 -0.3225 -0.0225  0.1596  5.1775 
## 
## Coefficients:
##             Estimate Std. Error t value             Pr(>|t|)    
## (Intercept) 0.407333   0.119890   3.398              0.00108 ** 
## GT          0.083038   0.006378  13.020 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8382 on 77 degrees of freedom
##   (2 observations deleted due to missingness)
## Multiple R-squared:  0.6876, Adjusted R-squared:  0.6836 
## F-statistic: 169.5 on 1 and 77 DF,  p-value: < 0.00000000000000022

Which implies, for a GT of 8.5: 46381.4444572

Mileage

We know (look at trip_info) that on average a small boat goes max distance 236.8060 km from port. Assuming then that fishing costs no gas consumption and that all the gas consumed in the survey is just going back and forth once we get $:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##  0.4223  0.6493  1.2669  2.5918  1.7683  8.4457       1

Let’s focus on the median (there are some big outliers): 1.2669 l/km

Speed

Assuming 13kph (7 knots)

Catchability

To calibrate.

Exploration probability

Assuming folks are explore-exploit-imitate it turns out that most people agree on having a fixed exploration probability:

##  No Yes 
##   6  18
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    5.00   20.00   25.00   28.33   40.00   50.00       6

Population 2: Medium longliners

A smaller population, accounting for about a third of the small dropline landings is the medium longliners; almost all concentrated in Bajomulyo

Registration Port Frequency
PP. Bajomulyo 54
PP. Karangsong 5
Probolinggo 9

The survey really has only 6 boats that qualify as medium longliners, unfortunately none in 712.

Rest Time & Yearly Effort

Assume max 200 days out (4800 hours), no seasonality

Max Trip Length

Again, about 12 days out

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    8.00    9.75   12.50   11.67   13.00   15.00

Size of hold

Use formula from hold_size.pdf:

## [1] 6906.524

Which I will round to 6900.

None of them has a fixed target income, mostly trying to get a proportion of the operating costs back.

Variable Cost

Using the regression (since there are so few respondents): 106929.8444757

Mileage

We know (look at trip_info) that on average a small boat goes max distance 225.6450 km from port. Assuming then that fishing costs no gas consumption and that all the gas consumed in the survey is just going back and forth once we get $:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.330   1.357   1.440   1.459   1.440   1.773

Let’s focus on the median (there are some big outliers): 1.440 l/km.

This, I think, is a bit too low because we have data on 15-16GT longliners but we want to model 26GT boats instead.

Speed

Assuming 13kph (7 knots)

Catchability

To calibrate.

Exploration probability

Assuming folks are explore-exploit-imitate it turns out that most people agree on having a fixed exploration probability:

##  No Yes 
##   2   4
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    10.0    17.5    20.0    22.5    25.0    40.0       2

Population 3: Big longliners

There are a few big longliners, they make up only half of the medium longliners landings (and a seventh of the small dropliners) but still significant since they are all concentrated in a few boats.

Unfortunately we only have 4 observations, but all from Probolinggo.

Registration Port Frequency
PP. Bajomulyo 21
Probolinggo 3

Rest Time & Yearly Effort

Assume max 200 days out (4800 hours), no seasonality

Max Trip Length

These guys stay out for months

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##      60      60      60      60      60      60

Size of hold

Use formula from hold_size.pdf (assuming 42 as GT):

## [1] 13498.56

Which I will round to 13500

Variable Cost

Using the regression (since there are so few respondents): 162288.3816355

Mileage

We know (look at trip_info) that on average a small boat goes max distance 528.8952 km from port. Assuming then that fishing costs no gas consumption and that all the gas consumed in the survey is just going back and forth once we get $:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   12.29   13.71   14.65   19.85   20.80   37.81

This is way too high, however it matches Bastardie’s formula 5.9987067 assuming a 1000HP engine (which still feels too powerful, but it’s the only survey answer we got)

Speed

Assuming 13kph (7 knots)

Catchability

To calibrate.

Exploration probability

Assuming folks are explore-exploit-imitate it turns out that most people agree on having a fixed exploration probability:

## Yes 
##   4
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     5.0     6.5    18.5    18.0    30.0    30.0

Biomass

Let’s pretend 712 can be isolated biologically and socially, such that we have a single fisher landing 13495.5 tonnes a year.

Assuming a low resilience and a guess of average \(\frac {B_{2014}}{K} \approx \frac {B_{2018}}{K} \in [.15,.25]\) we can run Catch-MSY and look at the result. Because of the low spread around \(\frac {B_{t}}{K}\) the result is a quite optimistic outlook with \(K \approx 300,000 t\) and a collapse predicted 8.5 years at current catch levels.

## Possible combinations =  35287 
## geom. mean r = 0.262 
## r +/- 2 SD = 0.091 - 0.753 
## geom. mean k = 298231 
## k +/- 2 SD = 185710 - 478928 
## geom. mean MSY = 19517 
## MSY +/- 2 SD = 8160 - 46679

If we increase uncertainty \(\frac {B_{2014}}{K} \approx \frac {B_{2018}}{K} \in [.10,.30]\) we get a collapse within 4.5 years.

## Possible combinations =  37536 
## geom. mean r = 0.296 
## r +/- 2 SD = 0.102 - 0.86 
## geom. mean k = 188961 
## k +/- 2 SD = 135761 - 263009 
## geom. mean MSY = 13984 
## MSY +/- 2 SD = 5548 - 35244

Calibration

Optimistic

Let’s start with the optimistic model. We would like the catches in year 2014-2018 to be about right at about 13495.5, properly subdivided between populations. We start the model in 2014, we can get the biomass by stepping backward:

Biomass Year
59646.15 2018
62433.49 2017
64808.18 2016
66837.99 2015
68577.93 2014

This implies \(\frac{B_{2014}}{K} \approx .23\)

We calibrate catchability of the fleet, we can compare simulated and real:

We get more or less the right landings, with small dropliners showing more variability year to year.

If we do a bit of forecast we see that the collapse will not occur in POSEIDON (or at least, not within 10 years). This is because the stock gets depleted enough that CPUE and landings are affected:

Pessimistic

Again, assuming in 2018 we are at 20% of \(K\), backtrack to 2014. This time with the pessimistic \(K,r\) combinations

Biomass Year
37792.20 2018
43763.18 2017
48766.75 2016
53011.17 2015
56649.73 2014

That implies that in 2014 the biomass was at about 30% of \(K\). This is a “better” starting point than the optimistic world but it’s only so because the biological parameters are weaker to shocks.

Again, collapse is slower in POSEIDON because agents struggle to keep landings at a constant rate, however in the pessimistic scenario you do get to basically depleted biomass by year 2028.

Policy

Optimistic

Fixed Season \(\geq\) 5GT

Fixed Season \(\geq\) 30GT

Pessimistic

Fixed Season \(\geq\) 5GT

Fixed Season \(\geq\) 30GT